我有兩題數學要大家幫手

a)
Consider △ACH,
tan 60° = h / AC
AC = h / tan 60°
AC = h / sqrt 3 //

Consider △BCH,
tan 30° = h / BC
BC = h / tan 30°
BC = h / (1 / sqrt 3)
BC = (sqrt 3)h //

As AB=AC+BC,thus AB = h / sqrt 3 + (sqrt 3)h
　　　　　　　　　　 = 4h / sqrt 3 //

b) using the result of (a), AB = 4h / sqrt 3
　　　　　　　　　 2000 = 4h / sqrt 3
　　　　　　　　　　　 h = 2000(sqrt 3)/4
　　　　　　　　　　　　 = 500(sqrt 3)
　　　　　　　　　　　　 = 866m // (cor. to the nearest m)

2007-04-08 12:13:24 補充：
樓上那位,你說AC = (tan60)h , BC = (tan30)h那 AC 豈不是會大過BC?但按常理,angle of elevation(仰望角)越大,代表那物件越高, 或水平距離越近所以, AC

2007-04-08 12:14:50 補充：
所以, AC

2007-04-08 12:18:36 補充：
所以, AC 小於 BC 才是對的. (符號顯示不出)另外,tan x = "opposite side of x" / "adjacent side of x"至於你最終答案和我一樣,是因為tan 60° tan 30° = 1/tan 30° 1/tan 60°　　　　　　　　　　 = 1/tan 60° 1/tan 30°所以,你倒置了兩個tan 對答案沒有影響.但問題出於AC和BC的數值身上.而我的答案, AC = h / sqrt 3 和 BC = (sqrt 3)h 才是對的.

a>
consider triangle ACH
AC / h = tan60
AC = (tan60)h

consider triangle BCH
BC / h = tan 30
BC = (tan30)h

AC + BC = AB
so AB = (tan 60)h + (tan30)h
= h(tan 60 + tan30)

b>
sqrt means square root

h(tan 60 + tan30) = 2000

we know that tan 60 = sqrt(3)
and tan 30 = 1 / sqrt(3)

h = 2000 / (sqrt(3) + 1 / sqrt(3))
= sqrt(3) 2000 / (3 + 1) (multiply both quotient and divisor by sqrt(3))
= 500 sqrt(3)

2007-04-08 12:44:20 補充：
係喎, 調轉o左唔好意思